olymmath

JBMO-SL 2011 C6

Let n>3n>3 be a positive integer. An equilateral triangle △ABC\triangle A B C is divided into n2n^{2} smaller congruent equilateral triangles (with sides parallel to its sides).

Let mm be the number of rhombuses that contain two small equilateral triangles and dd the number of rhombuses that contain eight small equilateral triangles. Find the difference m−dm-d in terms of nn.

Dataset text NuminaMath olympiads. Quoted with source.

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6n-9

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